劉青山 楊 淼 譚志誠,2,* WELZ-BIERMANN Urs,*

(1中國科學院大連化學物理研究所,中國離子液體實驗室,遼寧大連 116023; 2中國科學院大連化學物理研究所,熱化學實驗室,遼寧大連 116023)

ILs as organic salts,often exhibit interesting properties,such as low melting points,good solvation properties,and nonvolatility,which are required both by industrial and scientific communities for their broad application range as electrolytes in batteries and supercapacitors[1-2],reaction media in nanoscience[3], physical chemistry[4-5]and many other areas.Therefore,the data of physicochemical properties of ILs are fundamental for their future application and valuable for an insight into the origins of their unique behavior.Recently,more and more publications reported the experimental physicochemical properties of various ILs[6-15].Although there is a significant amount of data related to imidazolium-based ILs,properties of homologue of[Cnmim] [EtSO4],[Cnmim][OcSO4],and[Cnmim][NTf2](n=1-6)covered inthis publication are still limited[16-17].In this regard,we estimated various physicochemical properties of[C2mim][EtSO4],[C4mim] [OcSO4],and[C2mim][NTf2]by using their experimental density and surface tension data.In the next step,the physicochemical properties of their homologues[Cnmim][EtSO4],[Cnmim][OcSO4], and[Cnmim][NTf2](n=1-6)were predicted from the estimated values of their molecular volumes and parachors.In the present paper,the ionic liquid cations are 1-alkyl-3-methylimidazolium ([Cnmim]+),tetra-alkyl ammonium([TAA]+),N-octyl-3-methylpyridinium([m3opy]+);the anions of the ILs are ethylsulfate ([EtSO4]-),octylsulfate([OcSO4]-),bis(trifluoromethylsulfony) imide([NTf2]-),and tetrafluoroborate([BF4]-).

1 Volumetric,entropy and lattice energy

The molecular volume,Vm,can be calculated from experimental density using the following equation: where M is molar mass,ρ is density,and N is Avogadro′s constant.

According to Glasser′s theory[18],the standard molar entropy, S?,could be estimated from the following equation:

The lattice energy,UPOT,was estimated according to the following equation[18]:

The contribution methylene(—CH2—)group to the molecular volume is 0.0272 nm3for[Cnmim][BF4][18],0.0282 nm3for [Cnmim][NTf2][18],0.0270 nm3for[Cnmim][AlCl4][15],and 0.0278 nm3for[Cnmim][Ala][14].Due to the similar values of the contribution of per—CH2—to the molecular volume,the group of methylene in the alkyl chains of the imidazolium-based ILs could be considered to have the similar chemical environment.Hense, the mean value of the contribution can be calculated to be 0.0275 nm3,the physicochemical properties(density,standard entropy, latticeenergy)of the homologues of[Cnmim][EtSO4]and[Cnmim] [OcSO4](n=1-6)could be predicted.Using the value 0.0282 nm3for the contribution of per—CH2—to the molecular volume for the homologues of[Cnmim][NTf2](n=1-6)[18],the physicochemical properties of all IL homologues can be predicted.The calculated density value(1.4381 g·cm-3)for[C4mim][NTf2]is in good agreement with the experimental values(1.4366 g·cm-3[6], 1.43410 and 1.43573 g·cm-3[19]).The predicted density value (1.0881 g·cm-3)for[C2mim][OcSO4]is also in good agreement with the experimental value of 1.0942 g·cm-3[20].

All of these estimated and predicted physicochemical property data are listed in Tables 1-3.

Based on the plots of S?against the number of the carbons,n, in the alkyl chain of the ILs(see Fig.1),the contribution of per methylene group to S?was calculated to be 35.1 J·K-1·mol-1for [Cnmim][NTf2],34.3 J·K-1·mol-1for[Cnmim][EtSO4],and 34.3 J·K-1·mol-1for[Cnmim][OcSO4].The above calculated values are in good agreement with the literature values of 35.1 J·K-1·mol-1for[Cnmim][NTf2][18],33.9 J·K-1·mol-1for[Cnmim][BF4][18],33.7 J·K-1·mol-1for[Cnmim][AlCl4][15],and 34.6 J·K-1·mol-1for [Cnmim][Ala][14].According to these various values for the contribution of per methylene group to the standard molar entropy in the homologue series with different anions,it could be concluded that these contributions are relatively similar for all imidazolium-based ILs.

2 Parachors and molar enthalpy of vaporization

The parachor,P,was estimated from the following equation[21]:

where γ is the surface tension.

According to literature[15],the contribution of per methylene (—CH2—)group to parachor is 31.1.The values of parachors for the homologue series of the imidazolium-based ILs[Cnmim] [EtSO4],[Cnmim][OcSO4],and[Cnmim][NTf2](n=1-6)were predicted.

The values of molar enthalpies of vaporization were estimated in terms of Kabo′s empirical equation[22]:

where V is molar volume.

According to Eq.(4),the surface tension can be calculated from predicted density and parachor data.The calculated value(31.71 mJ·m-2)for the surface tension of[C4mim][NTf2]is in good agr-eement with the experimental value(32.80 mJ·m-2)[6].The molar enthalpy of vaporization,,then can be obtained based on the predicted density and surface tension data.

Table 1 Estimated and predicted values of physicochemical properties of[Cnmim][EtSO4](n=1-6)at 298.15 K

Table 2 Estimated and predicted values of physicochemical properties of[Cnmim][NTf2](n=1-6)at 298.15 K

Table 3 Estimated and predicted values of the physicochemical properties of[Cnmim][OcSO4](n=1-6)at 298.15 K

All of these data are listed in Tables 1-4.

Fig.1 Plots of S?against the number of the carbon(n)in the alkyl chain of the ILs at 298.15 K(a)S?=570.7+34.27n,R=0.9999 for[Cnmim][OcSO4]; (b)S?=492.7+35.14n,R=0.9999 for[Cnmim][NTf2]; (c)S?=355.2+34.29n,R=0.9999 for[Cnmim][EtSO4]

The plots of density,ρ,and surface tension,γ,against the number of carbon,n,in alkyl chain of ILs at 298.15 K are shown in Figs.2 and 3.

FromtheFigs.2and3,itcanbeseenthatasfordensity:[Cnmim] [NTf2]>[Cnmim][EtSO4]>[Cnmim][OcSO4]and as for surface tension:[Cnmim][EtSO4]>[Cnmim][NTf2]>[Cnmim][OcSO4].

3 Interstice model theory

According to the interstice model[23-24],the interstice volume,v, could be estimated by classical statistical mechanics:

where kBis the Boltzmann constant,T is the thermodynamic temperature.

The molar volume of ionic liquids,V,consists of the inherent volume,Vi,and the volume of the interstice;whereas the molar volume of the interstice is Σv=2Nv:

If the expansion volume of IL only results from the expansion of the interstice when the temperature increases,then,the thermal expansion coefficient,α,can be predicted from the interstice model:

Table 4 Values of the molar enthalpies of vaporization of ILs at 298.15 K

Fig.2 Plots of density(ρ)against n(n=1-6)at 298.15 K

All data obtained by this estimation and prediction are listed in Tables 1-3.

The prediction and estimation values of the thermalexpansion coefficients in Tables 1-3 are in good agreement with experimental values.It also can be noticed that the values of interstice fractions,Σv/V,differentiate only about 10%-15%for all ILs studied in the present article and these values are in good agreement with the values of volume expansion in the process from solid to liquid state for the majority of materials.Therefore the interstice model is applicable and the interstice model theory can be used to calculate the thermal expansion coefficient of imidazolium-based ILs.

4 Prediction of enthalpy of vaporization

Recently,Verevkin[25]has published an article titled“Predicting enthalpy of vaporization of ionic liquids:a simple rule for a complex property”,in which he predicted molar enthalpy of vaporization of ILs by a simple rule in case of lack of experimental data.He proposed the following simple rule:

where ΔHiis the contribution of the ith element,niis the number of the element of the ith type in ILs,ΔHjis the contribution of the jth structural correction and njis the number of the element of the jth structural correction in ILs.The parameters[25]for predicting the molar enthalpy of vaporization of ILs are listed in Table 5.

Verevkin pointed out that“a special structural correction couldbe also necessary for quaternary ammonium based ILs”[25].Herein,the structure of the quaternary ammonium cation is regarded to be the ring of imidazolium cation,therefore,its structural correction parameter is ΔH=27.1 kJ·mol-1.The predicted data are listed in Table 4.From this table,the values of the molar enthalpies of vaporization,predicted by Eq.(9)are in good agreementwiththe values estimated by Eq.(5)except for[C4mim] [OcSO4].This is because that the Eq.(5)is valid mainly for ILs [Cnmim][NTf2].Indeed,the assumption to consider the quaternary ammonium cation as a ring system needs confirmation.

Table 5 Parameters for predicting the enthalpy of vaporization of ILs at 298.15 K[25]

Fig.3 Plotsofsurfacetension(γ)againstn(n=1-6)at298.15K

5 Conclusions

The physicochemical properties(molecular volume,molar volume,parachor,interstice volume,interstice fraction,thermal expansion coefficient,standard entropy,lattice energy,and molar enthalpy of vaporization)of[C2mim][EtSO4],[C4mim][OcSO4], and[C2mim][NTf2]were estimated by using their experimental data of density and surface tension.Based on the estimated data of the molecular volume and parachor,the physicochemical properties(density,surface tension and all of the properties mentioned above)for their homologue series[Cnmim][EtSO4], [Cnmim][OcSO4],and[Cnmim][NTf2](n=1-6)were predicted.

We compared the values of molar enthalpies of vaporization for[C2mim][EtSO4],[C4mim][OcSO4],[C2mim][NTf2],[C4mim] [NTf2],[N4111][NTf2],[N8881][NTf2],and[m3opy][BF4],estimated by Kabo′s empirical equation with those predicted by Verevkin′s simple rule,and found that the values calculated in terms of the two approaches are in good agreement with each other.Hence,it is suggested that the molar enthalpy of vaporization of ILs could be estimated in terms of Verevkin′s simple rule when the experimental data are not available.

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